For many years, the Bayesian approach to statistical problems in the biomedical and biobehavioral sciences has been considered by many to be theoretically appealing, but of unproven benefit in practice. Recently, however, with the advent of modern computational techniques, Bayesian methods have begun to emerge as powerful tools for analyzing data in complex settings, such as clinical trials and longitudinal studies. Situations in which Bayesian methods are especially valuable are those where information comes from many similar sources, which are of interest individually and also need to be combined, so that hierarchical models may be constructed, evidence in favor of a particular model (possibly corresponding to a null hypothesis) must be assessed, modeling assumptions need to be examined systematically, or models are sufficiently complicated that inferences about quantities of interest require substantial computation. Concern for these general situations runs throughout the investigator's work. The basic objective is to advance relevant areas of applications in the biomedical sciences through the development and implementation of particular Bayesian methods. Thus, the specific aims are motivated by the general goal of bringing Bayesian methods to bear more effectively on practical problems that arise in applications in clinical trials, longitudinal studies, and meta-analysis. The work proposed to carry out these goals has many specific items, but several themes recur throughout: the investigator is interested in the behavior and application of hierarchical models; is developing and investigating methods for model selection using Bayes factors; is concerned about the possible sensitivity of posterior inferences to modeling specifications; and is attempting to take advantage of recent advances in Bayesian statistical computing. Throughout this application, the goal is to bridge the gap between theory and practice. To this end, several clinical investigations in which the investigator is involved are described and are used to motivate the work.